Richard Bright: You have spoken of complexity as being distinguished between ‘familiar’ or ‘normal’, and as ‘something else’. First of all, what is ‘familiar complexity’ and what is the ‘something else’?
Stuart Kauffman: Familiar complexity theory is now rather formulated and exploding in applications. The basic ideas include: nonlinear dynamical systems and their attractors, phase spaces, bifurcations and so on. In dynamical systems themselves is the emerging idea of “edge of chaos” or “criticality” which seems to apply to the brain and cell behaviors for many interesting reasons. There is also -
1) Fitness landscapes , fixed or time varying, of various statistical structures with means to search them, vast literature from genetic algorithm and simulated annealing and onward.
2) Agent based models from robotics to artificial life to models of ant colonies and termite colonies.
3) “Ensemble models” where the generic properties of some ensemble may predict “some” features of some system, physical, biological, economic, etc, but without knowing all the details of the system. May be very powerful and an unexpected outgrowth of statistical mechanics, examples spin glasses, random genetic network models etc.
4) Models of the origin of life and economic evolution where the models are not “Newton-like “efficient cause” models but seem to be “formal cause models independent of the physical or other “stuff” involved.
5) Structure of graphs and flows on them, from random to scale free to small world to others.
RB: What causes or drives the process of emergence?
SK: Many different definitions of “emergence” including:
1 Symmetry breaking in physics.
2, First and second order phase transitions in physics.
3. Collective behaviors of many variables hard to predict from detailed knowledge of underlying system.
4 New “properties” eg hydrogen atom and two water atoms make water, with so far unpredictable properties of liquid, surface tension, etc.
5. My own favourite, new grounds to think biological and technological and cultural evolution is “entailed by no law at all” so is radically emergent in its becoming. If true, it forces us beyond Newton, even Schrodinger, even Darwin, and may hint that the evolution of the biosphere is not even mathematizable, both no law and not mathematizable, if they hold up, are major negative results likely to drive new ways of thinking.
RB: Can you give an example of how an understanding of complexity advances a field of science?
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